Use the algorithm for curve sketching to sketch the following: а. у %3D х3 — 9х2 + 15х + 30 b. f(x) = -4r³ + 18x² + 3 %3D 1 с. у%3D 3 + d. f(x) = x4 – 4x3 8x2 + 48x %3D - (x + 2)2

Q: Integrate the following: dx J 4x2 + 1

A: ∫1x2+a2=1atan-1(xa)  Here we use u-subsitution .

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A: We need to find the length of remaining tubing piece.The lengths of cut pieces are,

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.